Charge and Lattice Fluctuations in Molecule-Based Spin Liquids

Abstract

Spin liquid (SL) systems have been the subject of much attention recently, as they have been theoretically predicted to not freeze, even at 0 K. Despite extensive searches being made for such a system, only a few candidates have been found. All of these candidates share geometrical frustrations that are based on triangular lattices. We applied vibrational spectroscopy to one of the candidates of a molecule-based SL system, and we compared its results against three antiferromagnetic compounds and four charge-ordered compounds. All of their structural motifs belong to triangular lattices. The C=C stretching modes in the SL state indicated that there were charge and lattice fluctuations. These fluctuations were suppressed but non-negligible in the AF compounds. This finding is potentially significant, as it indicates that a hidden lattice and charge fluctuation are the driving force of a geometrical frustration, which eventually leads to a SL state.

Figure 1

Molecular structure, crystal structure and schematic views of two-dimensional layers of β′–EtMe₃Sb[Pd(dmit)₂]₂ (Sb-salt 2). (a) Monomer of Pd(dmit)₂. (b) Crystal structure as viewed along the b-axis. (c) Two equivalent conducting layers with different orientations; layer 1 and layer 2. t _d, t _s and t _t denote the transfer integrals between neighboring dimers in the diagonal, stacking and transverse directions, respectively. (d) Schematic views of the two-dimensional layers.

Figure 2

Correlation diagram of C=C stretching modes in monomers, dimers, tetramers and octamers that have centre of inversion symmetries. The tetramers and octamers are composed of two and four dimers, respectively. The C=C stretching modes of the monomers and dimers are shown by the arrows. A_D–D_D: C=C stretching modes of a dimer, A_T1–D_T2: C=C stretching modes of a tetramer, and A_O1–D_O4: C=C stretching modes of an octamer. The positive and negative signs for each vibrational mode denote in-phase and out-of-phase vibrations, respectively. These C=C stretching modes are classified into Groups A–D. A_R-D_IR in the right column correspond to peaks in Fig. 3. C_O4 denoted by the blue area is independent of any C=C stretching modes of tetramer and dimer. A_IR and D_IR, denoted by green area, consist of C=C stretching modes of tetramer and octamer, but these are independent of any C=C stretching modes of dimer. A_IR consists of the A_T2 and A_O3 modes, and D_IR consists of the D_T2 and D_O3 modes. A_R, C_IR, B_IR and D_R, denoted by orange area, consist of C=C stretching modes of dimer, tetramer and octamer. A_R consists of the A_D, A_T1 and A_O1 modes, C_IR consists of the C_D, C_T1 and C_O1 modes, B_IR consists of the B_D, B_T1, B_O1 and B_O4 modes, and D_R consists of the D_D, D_T1, D_O1 and D_O4 modes.

Figure 3

IR and Raman spectra. (a) a-polarized IR spectra for Sb-salt 2. (b) b-polarized IR spectra for Sb-salt 2. (c) c*-polarized IR spectra of P-salt 1, Sb-salt 1 and Sb-salt 2. The a-polarized IR spectra of P-salt 2 is also shown in (c). (d) Raman spectra observed at 5 K. Aside from Sb-salt 2, all of the salts here have antiferromagnetic ground states. All of the IR spectra were obtained as conductivity spectra from the Kramers–Kronig transformation of the corresponding reflectance spectra.

Figure 4

HOMO–LUMO inversion, and charge distributions and bond alternations in a 2D layer of X[Pd(dmit)₂]₂. (a) Energy diagram of the monomers, normal dimer, and tight dimer. “L” and “H” represent the LUMO and HOMO of a monomer, respectively. The sum (+) and subtraction (−) between them designate bonding and antibonding interactions, respectively. (b) and (c): Two of three different CO states revealed by our previous works. (d): Layer consisting of regularly arranged [dimers]⁻. (e): Legend of electron densities of monomers in (b–d). The black, grey and white sections in the monomers of (b–d) denote the electron densities in the HOMO of (b) [tetramer]²⁻, (c) [octamer]⁴⁻ and (d) [dimer]⁻. Different patterns of the inter-dimer bond alternations; the bold, thin and dotted lines between the dimers denote the strong, intermediate and weak inter-dimer interactions, respectively, between the HOMOs in (b) [tetramer]²⁻ and (c) [octamer]⁴⁻. The interacting monomers that form tetramers or octamers in (b) and (c) are highlighted by the orange rectangles. Inter-dimer VBOs in (b) are formed along two of three directions in the triangular lattice. Intra-dimer charge separation in (b) is accompanied by inter-dimer VBOs. The intra-dimer interaction in a charge-rich dimer of (c) is weaker than that in a charge-poor dimer, which manifests itself as the intra-dimer VBO. Inter-dimer VBOs are also formed in (c). Intra- and inter-dimer charge separations of (c) are accompanied by inter- and intra-dimer VBOs, respectively. The combination between intra- and inter-dimer VBOs is formed along one of the three directions. There is no VBO in (d).